First principle study of optoelectronic and mechanical properties of lead-free double perovskites Cs₂SeX₆ (X = Cl, Br, I)

Abstract

The variant double perovskites are considered novel materials for solar cells and optoelectronic applications. Here, we explored electronic, mechanical, and optical characteristics of Cs₂SeX₆ (X = Cl, Br, I) by density functional theory (DFT) analysis. The tolerance factor between 0.97–1.0 signifies the structural stability of the investigated compounds while thermodynamic and mechanical stabilities were ensured by positive frequencies of phonon dispersion as well as elastic constants. Moreover, the Poisson and Pugh's ratios are explored for brittle and ductile behavior. The Debye and melting temperatures have also been reported through mechanical analysis. The tuning of the bandgap takes place from 3.10 to 2.64 eV and then 1.15 eV by substitution of Cl with Br and I, respectively. The optical spectra show a shift in absorption region from ultraviolet-to-visible. In addition, the low light reflection and optical energy loss range (0.0–3.0 eV) promises potential of the studied potential for solar cells and optoelectronics uses.

KEYWORDS:

• Perovskites
• solar cells
• optoelectronics
• structural stability
• Debye temperature

1. Introduction

To fulfil the stimulating demand for renewable energy in limited resources is very challenging. The conversion of electrical energy from heat or light energy sources is an essential requirement for renewable energy devices. The efficiency of such devices mainly depends on the selection of particular materials. Perovskite materials are intensively studied by researchers because of their potential applications [1–6]. From this versatile family of compounds, lead-halide-based solar cells have the highest efficiency reported to date [7]. A large number of configurations have been scrutinized of organic-based perovskites from which the formamidine lead triiodide (FAPbI₃) is found outstanding. Its power conversion efficiency (PCE) reaches 25.06% which is most suitable for solar cells [8]. Regardless of this achievement, Pb-based materials are not environmentally friendly. The replacement of Pb-based optoelectronic material with other non-hazardous material is still needed extensive research [9,10]. To fill this gap, a number of researchers have reported Pb-free single and double perovskite halides (DPH’s) [11]. In the case of simple perovskites, Parrey et al. [12] performed DFT calculations on RbGeI₃ and studied electro-optical properties. In another study on halides, Zhang et al. [13] investigated the electronic properties for CsGeX₃ (X = Cl, Br and I) and suggested optoelectronic applications of these compounds. Another strong candidate that emerged in the list of photovoltaic applications is vacancy-ordered double perovskite Cs₂SnI₆ reported recently [14]. The structure of vacancy-ordered double perovskites is A₂XY₆, where A is tetravalent and X octavalent cations, while Y is halides (Cl, Br or I). Exploring the hidden attributes of double perovskites useful for optoelectronic applications in industry, Wang et al. [15] have investigated a number of novel DPH’s and suggested possible solar cell applications. Among these materials, Sn- and Ge-based DPH’s are better alternatives of Pb-free materials in novel optical devices because they belong to the same group of Pb [16]. Experimentally Cs-based DPH’s were first prepared by Bagnall et al. [17]. In another study by Morss et al. [18], new Cs-based DPH’s were fabricated. Since the last decade, DPH’s have earned the name in the list of Pb-free compounds. Recently, Cs₂AgBiCl₆ and Cs₂AgBiBr₆ are cubic compounds reported that have shown remarkable optical applications in the visible range [19,20]. Furthermore, recently, the defective double perovskites Cs₂SeCl₆ and Cs₂TeCl₆ are elaborated for thermoelectric properties based on classical transport theory by BoltzTraP code. The computed lattice constants (10.18 and 10.51Å), formation energies (−23.56 and −24.13 eV), bandgaps (2.95 and 3.10 eV) and tolerance factor (0.728 and 0.725) are reported for Cs₂SeCl₆ and Cs₂TeCl₆, respectively [21].

The purpose of this study is to explore hidden traits of Cesium-based DPH’s for solar cell and thermoelectric applications. In this study, we have particularly focused on Cs₂SeX₆ (X = Cl, Br and I) DPH’s. Based on comprehensive literature survey, the electronic, elastic and optical properties of Cs₂SeX₆ (X = Cl, Br and I) DPH’s are scarcely being reported to date. We have used a state-of-the-art theoretical approach based on DFT to explore the aforementioned properties.

2. Method for calculations

The structural, electronic, elastic and optical properties of DPH’s were analysed by DFT based on the FP-LAPW method [22] performed in WIEN2k code [23]. Additionally, the exchange–correlation potential used in our study is Pardew Burke Ernzerhof Generalized Gradient Approximation (PBE-GGA) [24]. The PBE-GGA approximation solves the properties in the ground state with high precision; however, the calculated bandgap is underestimated. To circumvent this issue, the bandgap is improved by implementing modified Becke and Johnson Potential of Trans and Balaha (TB-mBJ) [25]. It improves the bandgap very accurately and the most versatile potential calculated through a mathematical equation. (1) $V_{x,\sigma }^{\text{mBJ}}(r)=c{V}_{x,\sigma }^{\text{BR}}(r)+(3c-2)\frac{1}{\pi }\frac{\sqrt{5}}{12}\frac{\sqrt{2t_{\sigma }(r)}}{{\rho }_{\sigma }(r)}$(1) where c is convergence factor, ${\rho }_{\sigma }(r)$ indicates density of states and $t_{\sigma }(r)$ denotes its kinetic energy. The charge convergence factor is calculated as (2) $c=\alpha +{\left(\beta \frac{1}{V_{\text{cell}}}\int d^{3}r\frac{|\mathrm{\nabla }\rho (r)|}{\rho (r)}\right)}^{\frac{1}{2}}$(2) where α and β are numeric constant and adjusted in WIEN2k. The number of K-points selected to achieve full convergence was set at 2000. This helped to generate a denser k-mesh of 12 × 12 × 12 k-mesh points. The maximum angular momentum value l_max was adjusted at 7. The R_MT × K_max was set to 8. Where R_MT and K_max are muffin-tin radii and cut-off wave vectors. Maximum Fourier transformation vector G_max was adjusted to 12. The self-consistent field (SCF) convergence was minimized up to 0.00001 Ry. The ground state optimizations of structural reforms were solved using the Murnaghan equation of state. Further, for phonon calculations, the density functional theory perturbation has been incorporated in the phonopy software to extract the phonon dispersion band structures [26].

3. Results and discussion

In this section, we have reported the structural, electronic, elastic and optical properties of DPH’s in detail. In Section 3.1, structural stability is explained under the Goldschmidt tolerance factor, ground state optimization and enthalpy of formation. Moreover, electronic properties are discussed which includes DOS and bandgap analysis. In Section 3.2, mechanical attributes of the studied compounds is being explained in detail. In the last section, optical properties are discussed to explore possible optical applications.

3.1. Structural reforms and electronic attributes

To calculate the DPH’s structural stability, ground state optimization of the compound is essential. In our study, we have used the Murnaghan equation of states to achieve equilibrium in structure. The stability in structure is addressed by using tolerance factor T_f of cubic crystal systems suggested by Goldschmidt [27]. (3) $T_f=\frac{r_{\text{Cs}}+r_{\text{X}}}{\sqrt{2}(r_{\text{Se}}+r_{\text{X}})}$(3) The T_f value around unity portrays cubic structure is stable. In our study, all compounds are stable in the cubic phase. The enthalpy of formation H_f of BPH’s is also calculated using (4) $H_f=E_{\text{(C}{\text{s}}_{\text{a}}\text{S}{\text{e}}_{\text{b}}{\text{X}}_{\text{c}}\text{)}}-(a{E}_{\text{cs}}+b{E}_{\text{se}}+c{E}_{\text{X}})$(4) All calculated values are summarized in Table 1. The negative value of H_f (Figure 1) ensures the thermodynamic stability of studied materials. Among the studied compounds, Cs₂SeCl₆ is more stable due to the large enthalpy of formation [28].

Figure 1. (Left) Ground state structural optimizations (a) Cs₂SeCl₆, (b) Cs₂SeBr₆, (c) Cs₂SeI₆. (Right) Crystalline structure of Cs₂SeX₆ (X = Cl, Br and I).

Table 1. Various calculated parameters, for instance, lattice constant a_o (Å), bulk modulus B_o (GPa), formation energy H_f (eV), electronic bandgap E_g (eV) and tolerance factor (T_f) of Cs₂SeX₆ (X = Cl, Br, I).

Parameters	Cs2SeCl6	Cs2SeBr6	Cs2SeI6
ao (Å)	10.70	11.37	12.31
Bo (GPa)	23.63	22.13	18.80
Hf (eV)	−1.55	−1.40	−1.35
Eg (eV)	3.10 (W-L)	2.64 (W-L)	1.15 (Γ-L)
Tf	0.97	0.98	1.0

The density functional perturbation theory (DFPT) has been incorporated to confirm the thermodynamic behaviour of the studied compounds. The computed dispersion plots are illustrated in Figure 2(a–c) which shows the studied compounds have positive frequencies. Therefore, the positive frequencies indicate the studied compounds are dynamically stable. Three acoustic modes of phonons dispersion are accurately zero at Γ symmetry direction which is also the confirmation of dynamical stability [29,30].

Figure 2. The phonon dispersion plots of (a) Cs₂SeCl₆, (b) Cs₂SeBr₆, (c) Cs₂SeI₆, respectively.

First, the structural, mechanical and thermodynamic stabilities are calculated according to their formalism as shown in the manuscript. However, we relate structural stability with mechanical and thermodynamic stabilities. The structural stability has been calculated from the tolerance factor which depends upon the atomic radii. Mechanical stability has been depicted from born mechanical stability criteria C₁₁< B < C₁₂, C₁₁–C₁₂>0 and C₄₄>0 [31]. Therefore, the bulk modulus is volumetric deformation after the applied stress and its value related to the lattice constant. The optimized lattice constant for stable structure and relaxed positions adjusts the bulk modulus to keep positive elastic constants for mechanical stability. Secondly, stable and relaxed structures released more energy which is measured in terms of negative formation energy. Therefore, stable structure measures are directly ensured from formation energy. Thirdly, the acoustic phonons have zero frequencies at Γ and L symmetries as depicted in the dispersion plot in Figure 2(a–c) which is confirmation of structural stability from the thermodynamic approach.

The electronic band structure of DPH’s is depicted in Figure 3. In this study, spin-polarized TB-mBJ potential is used to investigate the correlation effects. From Figure 3, all compounds have an indirect bandgap. The bandgap values are depicted in Table 1. It is observed that Cs₂SeI₆ has the smallest bandgap. The nature of the bandgap is further elaborated by the density of states (DOS) plot as shown in Figure 4. The valence band maxima are contributed mainly by the p orbital of the halogen atom in all compounds. While conduction band minima are formed by Se-p orbital. It can be inferred from the partial DOS that inter-band transition will occur only due to the involvement of Se-p to X-p orbitals.

Figure 3. Electronic band structure of (a) Cs₂SeCl₆, (b) Cs₂SeBr₆, (c) Cs₂SeI₆.

Figure 4. Total DOS and partial DOS of (a) Cs₂SeCl₆, (b) Cs₂SeBr₆, (c) Cs₂SeI₆.

3.2. Mechanical properties

The three elastic constants for the cubic crystals are prescribed as C₁₁, C₁₂ and C₄₄. These constants are calculated using the Charpin method embodied within the WIEN2k code. The stability criteria that cubic compound must satisfy are (C₁₁ > 0), (C₄₄ > 0), (C₁₁ − C₁₂ > 0), (C₁₁ + 2C₁₂ > 0) and (C₁₁ > B > C₁₂) [31]. From Table 2, all compounds satisfy the stability criteria. Using these elastic constants, we have calculated bulk modulus (B), Young’s modulus (E) and shear modulus (G) by formulas presented in Muhammed et al. [4]. It is found that Cs₂SeCl₆ has the highest B, G and E values which suggest that it is more rigid than Cs₂SeBr₆ and Cs₂SeI₆. To check whether the compound is ductile or brittle, the Pugh’s (B/G) criteria were used. If the value of B/G > 1.75, the studied material is considered ductile in nature; however, brittle otherwise. In our study, all compounds are found ductile. Additionally, its nature was also confirmed by Poisson’s ratio “υ” for which υ > 0.26 suggests the materials are ductile in nature. Moving further, the Kleinman parameter (ξ) [32] is used to estimate the bond strength whether it is bending or stretching. For ξ near 0, it suggests bond bending while for ξ around unity implies bond stretching. It is observed that Cs₂SeI₆ has the highest bond-stretching nature. To check the covalent and ionic nature of the bonds present in the unit cell Cauchy parameter $C^{\mathrm{\prime }\mathrm{\prime }}$ is computed as $C^{\mathrm{\prime }\mathrm{\prime }}=C_{12}-C_{44}$. The $C^{\mathrm{\prime }\mathrm{\prime }}<0$ portrays the dominancy of majority bonds as covalent. While for $C^{\mathrm{\prime }\mathrm{\prime }}>0$ ionic-bonding dominancy is expected. From analysis, all studied compounds exhibit positive value which reflects the dominancy of ionic bonding. It is found that Cs₂SeCl₆ has strong ionic nature than Cs₂SeBr₆ and Cs₂SeI₆. We have also checked the Debye temperature to estimate the influence of lattice stability in bonds among atoms by relation [33]. (5) $\mathrm{\Theta }=\frac{h}{k}{\left[\frac{3n}{4\pi }\left(\frac{N_A\rho }{M}\right)\right]}^{\frac{1}{3}}V$(5) where h and k are Plank’s and Boltzmann’s constant, ρ density of alloy, M molecular weight, N_A Avogadro number and n number of atoms. Also, V is total velocity computed by relation, (6) $V={\left[\frac{1}{3}\left(\frac{2}{v_t^3}+\frac{1}{v_l^3}\right)\right]}^{-\left(\frac{1}{3}\right)}$(6) where the longitudinal mode of velocity and transverse velocity is given by (7) $v_l=\sqrt{\frac{3B+4G}{3\rho }}\text{and}{v}_t=\sqrt{\frac{G}{\rho }}$(7) Ionic compounds exhibit high Debye and melting temperature which is affirmed by results and mentioned in Table 2. Melting temperature T_m [34] is estimated by relation (8) $T_m=412+[8.2\times (C_{11}+C_{12}^{1.25})]$(8) Thermal conductivity is used to understand the material response under influence of external heat. The minimum thermal conductivity is estimated by utilizing the Cahill criteria [35,36]. (9) $K_{\text{min}}=\frac{(k)}{2.48}(n_{\text{o}}{)}^{\frac{2}{3}}(v_{\text{l}}+2v_{\text{t}})$(9) where n_o is no of atoms per unit volume. The highest value of K_min is observed in the case of Cs₂SeCl₆ which suggests the material applications in high-temperature sensors. The hardness parameter H_a [37–40] is used to explain the property of a material to resist being dented under stress. It is calculated using the following relation, (10) $H_a=\frac{(1-2\upsilon )Y}{\upsilon (1+\upsilon )}$(10) All computed values are enlisted in Table 2 which suggests that Cs₂SeCl₆ has the highest ability to resist the applied stress.

Table 2. The calculated elastic constants (C₁₁, C₁₂ and C₄₄), bulk modulus B (GPa), shear modulus G (GPa), Young modulus E (GPa), Pugh’s ratio (B/G), Poisson ratio (υ), anisotropy factor (A), Kienman parameter (ξ), Lams constant (μ and λ), sound velocities V_ℓ, V_t and V (Km/s), Debye temperature _D (K), melting temperature T_m (K), hardness H_a (GPa) and minimum thermal conductivity K_min (Wm⁻¹K⁻¹) of Cs₂SeX₆ (X = Cl, Br, I).

Parameters	Cs2SeCl6	Cs2SeBr6	Cs2SeI6
C11 (GPa)	26.1	24.2	21.0
C12 (GPa)	22.4	21.1	19.20
C44 (GPa)	4.2	3.3	2.5
B (GPa)	23.63	22.13	19.80
G (GPa)	3.02	2.43	1.66
E (GPa)	8.69	7.05	4.85
B/G	7.81	9.08	11.9
υ	0.43	0.44	0.46
A	2.07	2.12	2.78
ξ	0.90	0.91	0.94
μ (GPa)	3.02	2.43	1.66
λ (GPa)	21.14	20.50	18.69
Vℓ (km s^−1)	3.025	2.61	2.364
Vt (km s^−1)	1.000	0.808	0.649
V (km s^−1)	1.137	0.921	0.740
D (K)	104.7	79.8	59.2
Tm (K)	700.3	675.0	671.1
Ha (GPa)	1.7	1.2	0.59
Kmin (Wm^−1K^−1)	0.105	0.078	0.058

Table 3. The calculated bandgap E_g (eV), static dielectric constant ε₁ (0), static refractive index n (0) and reflectivity R (0) of Cs₂SeX₆ (X = Cl, Br, I).

Compounds	Cs2SeCl6	Cs2SeBr6	Cs2SeI6
Eg (eV)	3.10	2.64	1.15
ε1 (0)	3.59	4.13	6.17
n (0)	1.89	2.03	2.48
R (0)	0.095	0.115	0.181

3.3. Optical properties

The optical behaviour of materials is strictly dependent on the interaction among light energy and matter, the transition rate of electrons from the valence-to-conduction bands, and the recombination rate. In the case of wide bandgap semiconductors, inter-band transitions are taken into consideration and intra-band transitions are ignored because excitation and recombination within the band are not possible [41]. We have analysed the optical spectra of Cs₂SeX₆ (X = Cl, Br, I) through graphical representation in Figures 5 and 6. The dielectric response has been explained by complex dielectric constant ε(ω) = Re ε(ω) + Im ε(ω), where Re ε(ω) is the real part of dielectric constant which enlighten the polarization and dispersion of light energy from lattice while its imaginary part Im ε(ω) describe the absorption of light energy when the frequency of light is greater than the threshold limit. The dependence of Re ε(ω) and Im ε(ω) is explained by the Kramer–Krong relation [42]. (11) $\begin{array}{rl}& \text{Re}\epsilon (\omega )=1+\frac{2}{\pi }P{\int }_0^{\mathrm{\infty }}\frac{{\omega }^{\mathrm{\prime }}{\epsilon }_2({\omega }^{\mathrm{\prime }})}{{{\omega }^{\mathrm{\prime }}}^2-{\omega }^2}d{\omega }^{\mathrm{\prime }}\end{array}$(11) (12) $\begin{array}{rl}& \text{Im}\epsilon (\omega )=\frac{e^2\hslash }{\pi m^2{\omega }^2}\sum _{v,c}{\int }_{BZ}[|M_{cv}(k)|\delta [{\omega }_{cv}(k)-\omega ]]d^{3}k\end{array}$(12)

Figure 5. (a) Real part of dielectric constant ε₁ (ω), (b) imaginary part of dielectric constant ε₂ (ω), (c) absorption coefficient α (ω) and (d) refractive index n (ω) of Cs₂SeX₆ (X = Cl, Br, I).

Figure 6. (a) Reflectivity R (ω), (b) optical loss factor L (ω) of Cs₂SeX₆ (X = Cl, Br, I).

The real dielectric constant Re ε(ω) elaborates the dispersion and polarization of light on interaction with the material of a slightly changing refractive index. The frequency of light depends upon phase velocity which reacts to maximum dispersion and polarized light at plasma resonance of lattice waves. The reported values of Re ε(ω) have been depicted in Figure 5(a). The zero-energy value static Re ε(0) of Cs₂SeCl₆ is 3.59 which increases to 4.13 and 6.17 by the replacement of Cl with Br and I because of decreasing bandgap values and large dispersion from Cl to I. The resonance frequencies occur at 3.3 eV (7.9), 2.80 eV (8.93) and 2.0 eV (11.7) for Cs₂SeCl₆, Cs₂SeBr₆ and Cs₂SeI₆, respectively. These are the peak values at which dispersion of light is maximum. Above the resonance frequency, the Re ε(ω) decreases to minimum at 3.69 eV (−0.22), 3.24 eV (1.12) and 2.97 eV (−4.84) for Cs₂SeCl₆, Cs₂SeBr₆ and Cs₂SeI₆, respectively. The two negative peaks for Cs₂SeCl₆ and Cs₂SeI₆ show the metallic behaviour for the light which reflects the light falling on the material in this region. Moreover, bandgap E_g and Re ε(0) are according to Penn’s model relation ε(0) ≈ 1 + (ħω_p/E_g)² [43].

The imaginary dielectric constant Im ε(ω) which measures the absorption of light energy is presented in Figure 5(b). The threshold values of absorption are noted as 3.1, 2.66 and 1.15 eV for Cs₂SeCl₆, Cs₂SeBr₆ and Cs₂SeI₆, respectively [44]. The maximum absorption peaks occur at 3. 54 eV (7.4), 3.09 eV (7.6) and 2.4 eV (15) for Cs₂SeCl₆, Cs₂SeBr₆ and Cs₂SeI₆, respectively which shows the absorption intensity of light increases from Cl to I and ultraviolet region is shifted to visible. Furthermore, absorption bandwidths 0.62 eV (3.2–3.8 eV), 0.75 eV (2.65–3.4 eV) and 1.36 eV (1.78–3.14 eV) increase from Cl to I which depict the Cs₂SeI₆ is optimal for absorption of light. The energy regions instigate the ultraviolet region of the spectrum for Cs₂SeCl₆, ultraviolet violet edge to the visible region for Cs₂SeBr_6, and the visible region of Cs₂SeI₆. Therefore, being a large absorption bandwidth in the visible region of light the Cs₂SeI₆ is the novel replacement of organic-based perovskites for solar cell applications. The ultraviolet region absorption of Cs₂SeCl₆ also makes them equally important for sterilizing surgical equipment and other optoelectronic devices.

Absorption coefficients α (ω) also explain the decline of light into the material similar to the imaginary dielectric constant, shown in Figure 5(c). The critical values of absorption coefficient 3.15, 2.66 and 1.16 eV for Cs₂SeCl₆, Cs₂SeBr₆ and Cs₂SeI₆, respectively. The peak values at 3.6 eV (5.8), 3.15 eV (5.9) and 2.61 eV (6.8) for Cs₂SeCl₆, Cs₂SeBr₆ and Cs₂SeI₆, respectively, show the maximum absorption similar like imaginary dielectric constant. In absorption coefficient, the shifting of peaks towards higher energy region and decreasing of intensities as compared to imaginary dielectric constant is the consequence conversion of dielectric constants into absorption coefficient which depend on frequency. The formula of absorption coefficient contains both real and imaginary parts of dielectric constants.

The refractive index n (ω) elucidates the dispersion of light and transparent behaviour of the material. The pattern of n (ω) and Re ε(ω) are similar and they are related to each other through relation $n^2-k^2=Re\epsilon (\omega )$. The calculated values of n (ω) are presented in Figure 5(d), which also explains the zero-frequency values n (0) and Re ε(0) that satisfied the relation $n_0^2=Re\mathcal{E}(0)$ as shown in Table 3. The peak values of refractive index are reported at 3.62 eV (1.6), 3.14 eV (1.61) and 2.56 eV (2.57) for Cs₂SeCl₆, Cs₂SeBr₆ and Cs₂SeI₆ halides, respectively. For the visible region, the refractive index lies between 2 and 3 [32] which confirms Cs₂SeI₆ is more suitable for visible region operation and its reducing intensity for Cs₂SeBr₆ and Cs₂SeCl₆ show the shifting of absorption from the visible region to the ultraviolet region.

The morphology of the materials depends upon the reflection of light which provides information about the roughness of the material surface. The calculated values of reflectivity have been presented in Figure 6(a). The reflection increases from zero-frequency value and reaches to maximum at 3.62 eV (0.31), 3.11 eV (0.32) and 3.09 eV (0.62) for Cs₂SeCl₆, Cs₂SeBr₆ and Cs₂SeI₆. Therefore, the reflection in the visible region is less as compared to the ultraviolet region. The optical loss of light energy in the form of scattering, heating, etc. has been reported in Figure 6(b). The optical loss of energy up to 3.0 eV is very negligible. Therefore, the optical characteristic analysis confirms the maximum absorption, less reflectivity and optical loss in the visible region increase the importance of studied materials for solar cells and other optoelectronic applications.

4. Conclusion

In the present article, the electronic, mechanical and optical properties are investigated thoroughly to understand the potential of the studied materials for solar cells and optoelectronics. The value of tolerance factor in the range (0.97–1.0) shows the structural stability while negative formation energy and positive frequencies of phonon dispersion certify thermodynamically stability. The studied materials are also mechanically stable and have ductile nature along with a high melting point. The Cs₂SeCl₆ has the highest absorption in the ultraviolet region and shifted to the visible region by substituting Cl with Br and I. The variant perovskites Cs₂SeI₆ is new potential material for visible light solar cells. Additionally, other parameters such as reflection of light and secondly the optical loss possess minimum value in the visible region. Therefore, the highest visible region absorption along with minimum loss of energy makes them interesting compounds for practical applications for solar cells and in optoelectronics.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Funding

This research was funded by the Princess Nourah bint Abdulrahman University Researchers Supporting Project number [PNURSP2022R29], Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for the financial support through the research groups program under grant number [R.G.P2/239/43].